EXTERNALITIES
Externalities
n An externality is a cost or a benefit imposed upon someone by actions taken by others. The cost or benefit is thus generated externally to that somebody.
n An externally imposed benefit is a positive externality.
An externally imposed cost is a negative externality.
n An externality will be viewed as a purely public commodity.
A commodity is purely public if
¨ it is consumed by everyone (nonexcludability), and
¨ everybody consumes the entire amount of the commodity (nonrivalry in consumption).
¨ E.g. a broadcast television program.
Examples of Negative Externalities
n Air pollution.
n Water pollution.
n Loud parties next door.
n Traffic congestion.
n Second-hand cigarette smoke.
n Increased insurance premiums due to alcohol or tobacco consumption.
Examples of Positive Externalities
n A well-maintained property next door that raises the market value of your property.
n A pleasant cologne or scent worn by the person seated next to you.
n Improved driving habits that reduce accident risks.
n A scientific advance.
Externalities and Efficiency
n Crucially, an externality impacts a third party; i.e. somebody who is not a participant in the activity that produces the external cost or benefit.
n Externalities cause Pareto inefficiency; typically
¨ too much scarce resource is allocated to an activity which causes a negative externality
¨ too little resource is allocated to an activity which causes a positive externality.
Inefficiency & Negative Externalities
n Consider two agents, A and B, and two commodities, money and smoke.
n Both smoke and money are goods for Agent A.
n Money is a good and smoke is a bad for Agent B.
n Smoke is a purely public commodity.
n Agent A is endowed with $yA.
n Agent B is endowed with $yB.
n Smoke intensity is measured on a scale from 0 (no smoke) to 1 (maximum concentration).
What are the efficient allocations of smoke and money?
n Suppose there is no means by which money can be exchanged for changes in smoke level.
n What then is Agent A’s most preferred allocation?
n Is this allocation efficient?
n Continue to suppose there is no means by which money can be exchanged for changes in smoke level.
n What is Agent B’s most preferred allocation?
n Is this allocation efficient?
n So if A and B cannot trade money for changes in smoke intensity, then the outcome is inefficient.
n Either there is too much smoke (A’s most preferred choice) or there is too little smoke (B’s choice).
Externalities and Property Rights
n Ronald Coase’s insight is that most externality problems are due to an inadequate specification of property rights and, consequently, an absence of markets in which trade can be used to internalize external costs or benefits.
n Causing a producer of an externality to bear the full external cost or to enjoy the full external benefit is called internalizing the externality.
n Neither Agent A nor Agent B owns the air in their room.
What happens if this property right is created and is assigned to one of them?
Case I:
Suppose Agent B is assigned ownership of the air in the room. Agent B can now sell “rights to smoke”.
Will there be any smoking?
If so, how much smoking and what will be the price for this amount of smoke?
n Let p(sA) be the price paid by Agent A to Agent B in order to create a smoke intensity of sA.
We can see from the diagram above that
i) Both agents gain and there is a positive amount of smoking.
ii) Establishing a market for trading rights to smoke causes an efficient allocation to be achieved.
Case II:
Suppose instead that Agent A is assigned the ownership of the air in the room.
Agent B can now pay Agent A to reduce the smoke intensity.
How much smoking will there be?
How much money will Agent B pay to Agent A?
We can see from the diagram above that
i) Both agents gain and there is a reduced amount of smoking.
ii) Establishing a market for trading rights to smoke causes an efficient allocation to be achieved.
n Notice that
- The agent given the property right (asset) is better off than at her own most preferred allocation in the absence of the property right.
- Amount of smoking that occurs in equilibrium depends upon which agent is assigned the property right.
Coase’s Theorem
n Is there a case in which the same amount of smoking occurs in equilibrium no matter which agent is assigned ownership of the air in the room?
n Coase’s Theorem: If all agents’ preferences are quasilinear in money, then the efficient level of the externality generating commodity is produced no matter which agent is assigned the property right.
From previous graph, the same amount of smoking occurs in equilibrium no matter which agent is assigned ownership of the air if, for both agents, the MRS is constant as money changes, for given smoke intensity.
So, for both agents, preferences must be quasilinear in money; U(m,s) = m + f(s).
Production Externalities
n A steel mill produces jointly steel and pollution.
n The pollution adversely affects a nearby fishery.
n Both firms are price-takers.
pS is the market price of steel.
pF is the market price of fish.
Steel Firm Problem
n cS(s,x) is the steel firm’s cost of producing s units of steel jointly with x units of pollution.
and
If the steel firm does not face any of the external costs of its pollution production then its profit function is
and the firm’s problem is to
The first-order profit-maximization conditions are
and
states that the steel firm should produce the output level of steel for which price = marginal cost.
is the rate at which the firm’s internal production cost goes down as the pollution level rises
is the marginal cost to the firm of pollution reduction.
What is the marginal benefit to the steel firm from reducing pollution?
Zero, since the firm does not face its external cost.
Hence the steel firm chooses the pollution level for which
Example
Suppose cS(s,x) = s2 + (x - 4)2 and pS = 12. Then
F.O.Cs are
and
pS = 12 = 2s determines the profit-max output level of steel; s* = 6
-2(x – 4) is the marginal cost to the firm from pollution reduction. Since it gets no benefit from reducing pollution, it sets x* = 4
The steel firm’s maximum output level is thus
Fishery Problem
n The cost to the fishery of catching f units of fish when the steel mill emits x units of pollution is cF(f, x).
and
Given f, cF(f, x). increases with x; i.e. the steel firm inflicts a negative externality on the fishery.
The fishery’s profit function is
so the fishery’s problem is to
F.O.C. is
Higher pollution raises the fishery’s marginal production cost and lowers both its output level and its profit.
This is the external cost of the pollution.
Example
Suppose cF(f, x). = f2 + xf and pF = 10.
The external cost inflicted on the fishery by the steel firm is xf.
Since the fishery has no control over x it must take the steel
firm’s choice of x as a given.
The fishery’s profit function is thus
Given x, the first-order profit-maximization condition is
So, given a pollution level x inflicted upon it, the fishery’s profit-maximizing output level is
Notice that the fishery produces less, and earns less profit, as the steel firm’s pollution level increases.
The steel firm, ignoring its external cost inflicted upon the fishery,chooses x* = 4, so the fishery’s profit-maximizing output level given the steel firm’s choice of pollution level is
f* = 3, giving the fishery a maximum profit level of
Notice that the external cost is $12.
n Are these choices by the two firms efficient?
n When the steel firm ignores the external costs of its choices, the sum of the two firm’s profits is $36 + $9 =$45.
n Is $45 the largest possible total profit that can be achieved?
Merger and Internalization
n Suppose the two firms merge to become one. What is the highest profit this new firm can achieve?
What choices of s, f and x maximize the new firm’s profit?
The first-order profit-maximization conditions are
The solution is
and the merged firm profit level is
This exceeds $45, the sum of the non-merged firms.
n Merger has improved efficiency.
n On its own, the steel firm produced x* = 4 units of pollution.
n Within the merged firm, pollution production is only xm = 2 units.
n So merger has caused both an improvement in efficiency and less pollution production. Why?
n But why is the merged firm’s pollution level of xm = 2 efficient?
n The external cost inflicted on the fishery is xf, so the marginal external pollution cost is
n The steel firm’s cost of reducing pollution is
Efficiency requires
n Merger therefore internalizes an externality and induces economic efficiency.
n How else might internalization be caused so that efficiency can be achieved?
Coase and Production Externalities
n Coase argues that the externality exists because neither the steel firm nor the fishery owns the water being polluted.
n Suppose the property right to the water is created and assigned to one of the firms. Does this induce efficiency?
n Suppose the fishery owns the water.
n Then it can sell pollution rights, in a competitive market, at $px each.
n The fishery’s profit function becomes
n Given pf and px, how many fish and how many rights does the fishery wish to produce? (Notice that x is now a choice variable for the fishery.)
First-order-conditions (profit maximization conditions) of the fishery are
And these give
Fish supply
Pollution right supply
n The steel firm must buy one right for every unit of pollution it emits so its profit function becomes
n Given pf and px, how much steel does the steel firm want to produce and how many rights does it wish to buy?
First-order-conditions (profit maximization conditions) of the steel firm are
And these give
Steel supply
Pollution right demand
Question: Would it matter if the property right to the water had instead been assigned to the steel firm?
Answer: No. Profit is linear, and therefore quasi-linear, in money so Coase’s Theorem states that the same efficient allocation is achieved whichever of the firms was assigned the property right. (And the asset owner gets richer.)
The Tragedy of the Commons
n Consider a grazing area owned “in common” by all members of a village.
n Villagers graze cows on the common.
n When c cows are grazed, total milk production is f(c), where f' 0 and f'' 0.
n How should the villagers graze their cows so as to maximize their overall income?
n Make the price of milk $1 and let the relative cost of grazing a cow be $pc.
Then the profit function for the entire village is
and the village’s problem is to
The income-maximizing number of cows to graze, c*, satisfies
i.e. the marginal income gain from the last cow grazed must equal the marginal cost of grazing it.
n For c = c*, the average gain per cow grazed isbecause f' > 0 and f'' < 0. So the economic profit from introducing one more cow is positive.
n Since nobody owns the common, entry is not restricted.
n Entry continues until the economic profit of grazing another cow is zero; that is, until
n The reason for the tragedy is that when a villager adds one more cow his income rises (by f(c)/c - pc) but every other villager’s income falls.
n The villager who adds the extra cow takes no account of the cost inflicted upon the rest of the village.
n Modern-day “tragedies of the commons” include